[Python-3000] Breakthrough in thinking about ABCs (PEPs 3119 and 3141)

Jason Orendorff jason.orendorff at gmail.com
Tue May 1 06:32:04 CEST 2007

On 4/30/07, Guido van Rossum <guido at python.org> wrote:
> The correct
> approach is for TotallyOrdered to be a metaclass (is this the
> typeclass thing in Haskell?).

Mmmm.  Typeclasses don't *feel* like metaclasses.  Haskell types
aren't objects.

A typeclass is like an interface, but more expressive.  Only an
example has any hope of delivering the "aha!" here:

  -- This defines a typeclass called "Set e".
  -- "e" and "s" here are type variables.
  class Set e s where
      -- here are a few that behave like OO methods...
      size :: s -> Int    -- (size set) returns an Int
      contains :: s -> e -> Bool   -- (contains set element) returns Bool

      -- here are some where the two arguments have to be of the same type
      union :: s -> s -> s
      intersection :: s -> s -> s

      -- here's a constructor!
      fromList :: [e] -> s

      -- and here's a constant... with a default implementation!
      emptySet :: s
      emptySet = fromList []

Suppose someone has written a super-fast data structure for
collections of ints.  If I wanted to "register" that type as a Set, I
would write:

  instance Set Int FastIntSet where
      -- the implementation goes in here
      size self = ...implement this using FastIntSet magic...

More complex relationships among types are surprisingly easy to
express.  See if you can puzzle these out:

  instance Hashable e => Set e (HashSet e) where ...

  instance Cmp e => Set e (TreeSet e) where ...

  class PartialOrd t where
      (<=*) :: t -> t -> Bool

  instance (Set s, Eq s) => PartialOrd s where
      (a <=* b) = (intersection a b == a)

See?  It's nice.  But, eh, this is what typeful languages do
all day; they'd better be good at it.  :)


(Right now on a Haskell mailing list somewhere, a mirror image of me
is trying to explain what's so cool about zipfile.  Python wins.  ;)

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